Impact of In Vitro Experimental Variation in Kinetic Parameters on Physiologically Based Kinetic (PBK) Model Simulations

testing strategies as understanding them can improve the interpretation of in vitro toxicity results, allowing to estimate the internal plasma and tissue concentrations in humans after oral, dermal, or in-Research


Introduction
In 2020, the European Commission launched its EU Chemicals Strategy for Sustainability under the Green Deal. Key aspects of this strategy are to ban most harmful chemicals, to improve safe and sustainable chemicals by design, and to obtain a better account of potential "cocktail effects" (i.e., effects upon combined exposure) of chemicals (European Commission, 2019. Respective chemical safety data cannot only be obtained with traditional animal testing, which is costly and time-consuming and therefore not applicable to large numbers of compounds. Therefore, there is an increasing need for the regulatory use of animal-free testing strategies (Arnesdotter et al., 2021;Paul Friedman et al., 2020;de Boer et al., 2020). Absorption, distribution, metabolism and excretion of compounds, i.e., the kinetics, have a critical role in such animal-free testing strategies as understanding them can improve the interpretation of in vitro toxicity results, allowing to estimate the internal plasma and tissue concentrations in humans after oral, dermal, or in-

Impact of In Vitro Experimental Variation in Kinetic Parameters on Physiologically Based Kinetic (PBK) Model Simulations
Ans Punt 1 , Peter Bos 2 , Betty Hakkert 2 and Jochem Louisse 1 1 WFSR -Wageningen Food Safety Research, Wageningen, The Netherlands; 2 RIVM -The National Institute for Public Health and the Environment, Bilthoven, The Netherlands

Abstract
In vitro toxicokinetic data are critical in meeting an increased regulatory need to improve chemical safety evaluations towards a better understanding of internal human chemical exposure and toxicity. In vitro intrinsic hepatic clearance (CLint), the fraction unbound in plasma (fup), and the intestinal apparent permeability (Papp) are important parameters as input in a physiologically based kinetic (PBK) model to make first estimates of internal exposure after oral dosing. In the present study we explored the experimental variation in the values for these parameters as reported in the literature. Furthermore, the impact that this experimental variation has on PBK model predictions of maximum plasma concentration (Cmax) and the area under the concentration time curve (AUC0-24h) was determined. As a result of the experimental variation in CLint, Papp, and fup, the predicted variation in Cmax for individual compounds ranged between 1.4-to 28-fold, and the predicted variation in AUC0-24h ranged between 1.4-and 23-fold. These results indicate that there are still some important steps to take to achieve robust data that can be used in regulatory applications. To gain regulatory acceptance of in vitro kinetic data and PBK models based on in vitro input data, the boundaries in experimental conditions as well as the applicability domain and the use of different in vitro kinetic models need to be described in guidance documents.

Materials and methods
Data collection A literature search was performed to obtain an indication of the experimental variation in in vitro measured CL int , P app , and fu p . In case of CL int , the in vitro data collected by Louisse et al. (2020) were included in the present study. In that study, a literature search was performed to obtain an indication of the experimental variation in intrinsic clearance values obtained with primary hepatocytes, predominantly following the substrate depletion protocol. Given that the clearance data from Louisse et al. (2020) mainly covered pharmaceuticals, an additional literature search was performed in the present study to expand the chemical domain to include non-pharmaceuticals. To this end, Scopus 1 was used to identify papers or databases that provide relatively large datasets on in vitro metabolic clearances measured with primary hepatocytes.
For non-pharmaceuticals, the R httk database 3 (EPA) and Black et al. (2021) were identified as major sources for hepatic clearance data. For compounds for which two independent clearance measurements were found in these initial selected data sources, an additional search was performed with Google Scholar 4 to obtain additional clearance data from individual scientific papers.
Literature data were also collected to obtain an indication of the experimental variation in Caco-2 P app , and fu p values. Scopus was used to identify papers or databases that contain relatively large datasets of Caco-2 P app values or fu p values. The final selection of Caco-2 P app data was from Estudante et al. (2015), Gertz et al. (2010), Hallifax et al. (2012), Hou et al. (2004), Larregieu and Benet (2014), Lee et al. (2017), Li et al. (2007), and Neuhoff et al. (2003). In case of fu p , the R httk database (EPA) and data from Ye et al. (2016), Wang et al. (2014), Srivastava et al. (2021), Jones et al. (2021), Ferguson et al. (2019, Chen et al. (2019), and Deshmukh and Harsch (2011) were selected. Table 1 provides a summary of the data obtained with the literature search on in vitro intrinsic hepatic clearance as well as Caco-2 P app and fu p values for compounds from different chemical domains (pharmaceutical, chemical, food, cosmetic). A more extensive overview of the data and references is provided in supplementary file 1 2 .

PBK model predictions
For the compounds for which the experimental variation in all three parameters, i.e., CL int , P app , and fu p , could be determined (see Tab. 1), simulations were performed to explore the impact of the experimental variation on predictions of the maximum plasma concentration (C max ) and the area under the concentration time curve (AUC 0-24h ). For these simulations, a published generic human PBK model code by Jones and Rowland-Yeo (2013) was used. The original model code of Jones and Rowland-Yeo ations, as the combined effects of different kinetic processes determine the internal exposure. Therefore, data obtained with the different test systems need to be integrated, for example by PBK modelling (Louisse et al., 2017;Bessems et al., 2014;Choi et al., 2019), while taking the uptake and kinetics of various ports of entry (oral, dermal and inhalation) into account. To gain confidence in the outcomes obtained with PBK models that rely on in vitro input data, it is important to assess the robustness of the in vitro input data that are used and the combined impact of experimental variation in each of the individual parameters on the model predictions. In addition, each in vitro kinetic assay has its own inherent boundaries with respect to the conditions under which the in vitro experiments should be performed, including, for example, limitations with respect to the applied substrate concentration, enzyme concentration, or incubation time (Hubatsch et al., 2007;Gouliarmou et al., 2018;Seibert and Tracy, 2014). There are further restrictions with respect to the applicability domain of different in vitro kinetic studies. For example, in vitro kinetic constants, measured under linear conditions, can only be used for predictions at dose levels that would not lead to saturation of enzymes or transporters (Peters, 2012). To achieve regulatory use of in vitro kinetic studies, the robustness, experimental conditions under which the in vitro experiments need to be performed, and applicability domain of different in vitro kinetic studies need to be better understood.
Recently, Louisse et al. (2020) collected reported intrinsic hepatic clearance (CL int ) values from the literature for 30 compounds obtained with primary human hepatocytes as well as information on the experimental set-ups applied. They observed differences of up to two orders of magnitude in reported in vitro hepatic CL int values obtained from incubations with primary human hepatocytes and noticed that the experimental set-ups applied differed for many aspects between studies. Pooled hepatocytes were used in most studies, suggesting that differences between studies were not solely driven by interindividual differences in biotransformation activities (Louisse et al., 2020). Apart from the in vitro CL int values, the fraction unbound in plasma (fu p ), and the intestinal apparent permeability (P app ) are important parameters with which first estimates of internal concentrations can be made for oral exposure using a PBK model (Jones and Rowland-Yeo, 2013). Experimental uncertainties related to small differences in experimental set-ups can be expected for these input parameters.
The goal of the present study was to obtain an insight into the experimental variation in CL int , fu p , and P app and to explore the impact of this variation in the in vitro kinetic data on PBK model predictions. The results are discussed with respect to the importance of the development of guidance documents to 1) reduce experimental variation and 2) to equip regulatory bodies with the means to evaluate the quality of in vitro kinetic data and the adequacy of an in vitro study design.

Tab. 1: Model compounds and summary of in vitro kinetic data (mean, coefficient of variation (CV) and number of data entries (n)) collected for CLint, Papp, and fup
Number Compound a CLint (µL/min/10 6 cells) Papp (10 -6 cm/s) fup a For the compounds highlighted in bold, the experimental variation in all three parameters, i.e., CLint, Papp, and fup could be determined. b CV corresponds to the coefficient of variation (CV = SD/mean x 100%) and is used as indicator of the variation in the reported kinetic values.
To determine which of the in vitro input parameters contributed most to the predicted variation in C max and AUC 0-24h , a global sensitivity analysis was performed with RVis software (McNally et al., 2018;Loizou et al., 2021). To this end, for each compound, the R code of the PBK model was loaded into RVis 7 . Simulations were subsequently performed within the "Sensitivity" tab, using the e-FAST method, by adding the observed in vitro distributions (mean and CV) to the CL int , fu p , and P app parameters. Additional details on how these simulations were performed are provided in supplementary file 2 6 . The input data for the RVis simulations are provided in supplementary file 1 2 . Figure 1 shows the experimental variation in data from in vitro metabolic clearance studies as obtained from the literature. For many of the compounds, the CL int measurements vary over a 100-fold, generally ranging between values that are 5-fold higher and 20-fold lower than the mean of a specific compound. The results from Figure 1 reveal that the variation in CL int is consistent over the different types of compounds and chemical domains. The highest variations in in vitro CL int values are observed for the pharmaceuticals bosentan (19) and naproxen (12) with a respective 172-fold and 164-fold range in CL int values. However, a large variation is also found for the food-related compounds, exemplified for caffeine (7) and the food preservative 2,5-di-tert-butylbenzene-1,4-diol (38), with a 63-fold and 43-fold variation in in vitro reported CL int values, respectively.

Evaluation of the in vitro experimental variation in CL int values
(2013) was converted to R (R Core Team, 2021) and is provided on GitHub 5 . A description of the PBK model according to the OECD harmonized template is provided in supplementary file 2 6 . The code was modified with respect to the definition of the freely available concentration in the liver that is available for metabolism (C L *fu p ) to the more commonly used description (CV L *fu p ), in which CV L corresponds to the total concentration in the liver (C L ) divided by the liver:plasma partition coefficient (Grandoni et al., 2019). The generic PBK model consists of 13 compartments, corresponding to the major organs of the body and an arterial and venous blood compartment. The model requires chemical-specific parameters for 1) intestinal uptake, 2) partition coefficients, 3) the blood:plasma ratio, 4) the fraction unbound in plasma, and 5) hepatic clearance. Renal clearance is described in the model based on the glomerular filtration rate times the fraction unbound in plasma and does therefore not require any additional chemical-specific input parameter. The partition coefficients were calculated with the method of Rodgers and Rowland (2006). The blood:plasma ratio was assumed to be a fixed value of 1 for all compounds as there are currently insufficient data or calculators available to parameterize the blood:plasma ratio. The input parameters for the intestinal uptake, fraction unbound in plasma, and hepatic clearance were obtained from in vitro experiments as described above. To explore the impact of the variation in CL int , P app , and fu p on the C max and AUC 0-24h predictions, simulations were performed with all possible combinations of CL int , P app , and fu p for a specific compound. The codes to run these simulations are provided on GitHub 5 . The simulations were performed at a low single oral dose of 0.1 mg/kg bw at which linear clearance conditions can be expected for all compounds.  Figure 3 reveals the experimental variation in in vitro derived fu p values for a range of compounds. Given that the fu p values can only range between 0 and 1, as the fu p is a fraction, the extent of variation in the fu p estimates is less than observed for CL int and Caco-2 P app values as described above. The largest experimental variation is observed for diclofenac (36) with fu p values ranging from 0.0015-0.015, corresponding to a 10-fold range.

Impact of the combined variation in CL int , P app , and fu p on the PBK model-predicted C max and AUC 0-24h
For the seven compounds within the dataset for which CL int , P app , and fu p data from different studies were available, the combined effects of the experimental variation in the three input parameters on the PBK model predictions were determined. The This consistency in experimental variation over the range of different compounds provides an indication of the variation that can be expected from in vitro metabolic clearance studies with primary hepatocytes. Figure 2 shows the experimental variation in in vitro reported P app values. For the three compounds for which most Caco-2 P app measurements are available (i.e., metoprolol (13), verapamil (35), and antipyrine (1)), the variation in P app values appears to range over 13-to 60-fold, between values that are about 3-to 4-fold higher and about 4-to 15-fold lower than the mean P app value of a specific compound. Less data was available for the remaining compounds, and the results reveal a 1.5-to 5-fold variation. The depicted compounds are numbered as described in Table 1 and grouped into four categories from low to high CLint values. The depicted compounds are numbered as shown in Table 1 and grouped into four categories from low to high Papp values.

Evaluation of the in vitro experimental variation in Caco-2 P app values
range in predicted AUC 0-24h . A high variation in AUC 0-24h of 23-fold is also observed for the low-clearance compound caffeine (7). Figure 5 depicts the results of the global sensitivity analysis that was performed to determine which of the three input parameters (i.e., CL int , P app , or fu p ) contribute most to the variation in C max and AUC 0-24h predictions as observed in Figure 4. Experimental variation in CL int had the highest impact on AUC 0-24h predic-results of these predictions are depicted in Figure 4. For every chemical, each available CL int value was combined with each available P app value, and each CL int -P app combination was in turn combined with each available fu p value for a specific compound. Figure 4 reveals that the impact of the variation in experimental conditions on the PBK model predictions is different for each compound. The lowest variation in C max and AUC 0-24h predictions occurs for the low-clearance compound diazepam (6), revealing a 1.4-fold range in both C max and AUC 0-24h predictions. The highest variation in both C max and AUC 0-24h predictions occurs for the high-clearance compound verapamil (35), revealing a 28-fold range in predicted C max and a 23-fold

Fig. 3: Variation in in vitro fup (unitless) measurements
The histogram depicts the combined distribution of the variation over the different compounds. The presented values represent the normalized fup values, corresponding to the fup values obtained for a specific compound, divided by the mean of these values for the specific compound. The depicted compounds are numbered as shown in Table 1 and grouped into four categories from low to high fup values.

Fig. 4: Variation in PBK model-predicted C max (A) and AUC 0-24h (B) as a result of the variation in reported in vitro CL int , Papp, and fup values
The depicted compounds are numbered as described in Table 1.
reported in the publications. A more systematic analysis would be required to identify critical aspects of experimental designs, for example, by performing the in vitro kinetic studies with a full factorial design approach in which the impact of a number of variables in the experimental design is systematically studied (Maas et al., 2000). An incorrect design of in vitro kinetic experiments is expected to be one of the causes of the large variation in in vitro kinetic data present in the literature. For example, a critical aspect of in vitro clearance measurements with the substrate depletion protocol is that the applied concentration should be below the Michaelis-Menten constant K m (Black et al., 2021). However, measurements are still being published in which this condition is not met or not considered (e.g., Fortaner et al., 2021). In case of Caco-2 absorption experiments, a critical aspect for obtaining relevant P app values is that the experiments are performed under a concentration gradient, otherwise diffusion cannot take place. This means that the time-range in which the absorption studies are performed needs to be optimized to make sure that less than 10% of the compound is diffused to the basolateral compartment (also called sink conditions) (Usansky and Sinko, 2005). Such sink conditions provide the best representation of the physiological conditions as a concentration gradient between the gut lumen and the plasma will exist in vivo due to distribution of the chemical in the body after absorption. Examples are available in the literature in which the criterion of measuring under sink conditions is not met or not considered (e.g., Kulthong et al., 2018). In addition, factors that affect the concentration of a test item (solubility or plastic binding) will affect the results when not adequately taken into account (Fagerholm et al., 2021). Finally, data processing can also have a large effect on the derived kinetic constants. For example, mismatch-tions for all compounds and for four out of the seven compounds also on the C max predictions (caffeine (7), diltiazem (17), S-warfarin (9), and verapamil (35)). The observed variation in C max predictions for these compounds can thus largely be attributed to the variation in CL int . The experimental variation in uptake parameter P app has no influence on the AUC 0-24h predictions but does have an impact on the C max predictions of two out of the seven compounds (diazepam (6) and quinidine (18)). The relative sensitivity towards experimental variation in fu p values was found to be lower than for CL int (Fig. 5).

Discussion
With the present study we explored the experimental variation in in vitro CL int , Caco-2 P app , and fu p measurements and the impact that this experimental variation has on PBK model predictions of C max and AUC 0-24h . As a result of the observed experimental variation in CL int , P app , and fu p , the PBK model-predicted C max for the seven compounds for which all three parameters were available was found to range between 1.4-and 28-fold and the AUC 0-24h to range between 1.4-to 23-fold. The large variation in C max and AUC 0-24h predictions, as observed for some of the compounds, indicates that the in vitro kinetic data are currently difficult to use in a regulatory context, since there are currently no means to evaluate the adequacy of a given in vitro kinetic experimental design used to obtain PBK model input parameters. At present, insufficient data are available to elucidate the underlying causes for the experimental variation, as often critical experimental details, like solubility experiments and linearity checks (rate constants linear with time or concentration), are not

Fig. 5: Relative sensitivity of the C max (A) and AUC 0-24h (B) prediction to the variation in CL int , P app , and fu p , as obtained with the RVis global sensitivity analysis
The relative sensitivity represents the relative contribution of each of the three parameters to the variation in Cmax or AUC0-24h as observed in Figure 4. For example, in case of caffeine (7), the variation in CLint accounted for 87% of the total variation in Cmax predictions, whereas variation in fup and Papp contributed 6% and 1.8%, respectively. The remaining 5.2% variation is caused by the interaction between these different parameters as depicted in the supplementary file 2 6 . domain of different in vitro kinetic studies to meet specific regulatory needs. The in vitro kinetic data discussed in the present study can, for example, only be used to make first-tier estimates of plasma concentrations of the parent compound after oral exposure (Jones and Rowland, 2013). Simulations of inhalation and dermal exposure will require additional kinetic input data on in vitro lung and dermal absorption to mimic these respective exposure routes. The first-tier estimates of plasma C max and AUC 0-24h in the present study after oral exposures also do not yet take the contribution of metabolites, possible saturation of biotransformation enzymes, possible involvement of transporters, or possible extrahepatic metabolism into account. At present it remains particularly difficult to determine when additional kinetic processes, like transporter kinetics or extrahepatic metabolism, need to be considered for a specific compound (Sager et al., 2015). Additional research is still needed to define the characteristics of chemicals that require the inclusion of these kinetic processes in PBK models (Punt et al., 2022).
Whereas the present study focused on the impact of variation in reported in vitro CL int , fu p , and P app values on PBK model predictions, other in vitro kinetic input parameters could be relevant as well. Metabolic clearance is, for example, measured not only with primary hepatocytes but also with liver microsomes and S9. In addition, in situations where dose-dependent kinetics are of importance, the Michaelis-Menten constants (K m and V max ) need to be derived from the in vitro metabolism studies. Moreover, in vitro transporter kinetic data (e.g., intestine, kidney, and liver transporters) are important for the kinetics of some compounds. A similar variability in experimental results may be expected for each of these in vitro methods if non-standardized approaches are used, and a description of experimental boundaries and the applicability domain will be needed. For example, the variability reported in the literature for metabolic clearance rates for bisphenol A with human liver microsomes ranges 30-fold (from 0.078 to 2.36 mL/min/mg microsomal protein) (Mazur et al., 2010;Elsby et al., 2001;Hanioka et al., 2020), which is similar to the overall variability in hepatocyte clearance data as observed in the present study. Apart from the in vitro kinetic data, in silico predictors of different kinetic parameters have been developed that may provide input data for PBK models. Particularly the prediction of partition coefficients (determining the distribution of compounds in different organs) depends on the use of these calculators, as these parameters are difficult to obtain with in vitro experiments. Recently, Punt et al. (2022) revealed that significant differences can occur as a result of the use of different calculators. For example, the calculation method of Berezhkovskiy (2004) frequently led to underpredictions of the C max of acidic compounds (pKa < 6), whereas the calculation method of Schmitt (2008) appeared to perform less well for highly lipophilic compounds (Punt et al., 2022). The calculation method of Rodgers and Rowland (2006) performed best overall and was therefore applied in the present study to predict the partition coefficients of the different compounds.
Overall, the results of the present study indicate a strong impact of experimental variation in CL int , P app , and fu p on PBK model-based C max and AUC 0-24h predictions. This implies that es between the observed data points and mathematical fit were observed in the present study for the compound 2,5-di-tert-butylbenzene-1,4-diol (38) (Wambaugh et al., 2019). Additional background information on critical aspects that need to be considered with respect to the design of in vitro kinetic studies is provided in supplementary file 2 6 .
Within a regulatory context, no guidance documents are currently available to be able to judge the quality of in vitro kinetic measurements, hampering the adequate performance of in vitro kinetic studies as well as the evaluation of data by end-users, including regulators. Recently, the OECD published a guidance document on a workflow for characterizing and validating PBK models (OECD, 2021). The quality of the in vitro input data is not yet explicitly taken into account in this guidance document. Nonetheless, effective protocols for performing in vitro kinetic studies to derive values for CL int , P app , and fu p are available in the scientific literature (e.g., Watanabe et al., 2018;Cai and Shalan, 2021;Hubatsch et al., 2007;Black et al., 2021). We highly recommend that these high-quality protocols are formalized to describe the applicability domain/use in a regulatory context. However, it should be noted that most of the protocols have been developed within the pharmaceutical domain, and most experience with the predictive performance of the different in vitro kinetic studies comes from the pharmaceutical domain. Compounds like pesticides, biocides, industrial chemicals, cosmetic ingredients, and food-related compounds generally have a broader range of physicochemical properties than pharmaceuticals and can contain, for example, compounds that are highly lipophilic or volatile (Andersen et al., 2019;Ferguson et al., 2019).
At present, in vivo experimental animal or human kinetic data are still requested in various regulatory guidelines (e.g., SCCS, 2018;EMA, 2018;OECD, 2021) to evaluate the performance of PBK models and to obtain confidence in the model predictions. However, this approach of model evaluations against in vivo data is mainly successful within the pharmaceutical domain as sufficient clinical data are only available for pharmaceuticals (EMA, 2018;Punt et al., 2017). For many other chemical domains, the availability of experimental animal or human in vivo kinetic data is limited, and evaluation against in vivo kinetic data is often not possible. Given that the combination of in vitro kinetic input data with PBK models provides a promising strategy to simulate the fate of chemicals in a body in the absence of in vivo kinetic data, it becomes crucial to find other means to gain confidence in the in vitro kinetic data and related PBK model predictions. The quality of the in vitro input parameters is important, as the model predictions will only be as good as the input. Application of uncertainty factors to the in vitro-based PBK model predictions might be one way to take the uncertainties related to the in vitro experimental variation into account. The results of the present study indicate, however, that large uncertainty factors may then be required to cover the impact of potential experimental variation. Increasing robustness of in vitro kinetic data and improving the possibilities within regulatory risk evaluations to assess the quality of in vitro kinetic data are therefore important next steps.
Apart from guidance documents on the design of in vitro kinetic studies, guidance will also be needed on the applicability as a key to the integrated toxicity risk assessment based primarily on non-animal approaches.  Coecke, S. et al. (2018).
Establishing a systematic framework to characterise in vitro methods for human hepatic metabolic clearance. Toxicol In Vitro 53, 233-244. doi:10.1016/j.tiv.2018.08.004 steps need to be taken to reduce experimental variation to increase the confidence in these in vitro kinetic data and related PBK model simulations for regulatory use. To this end, it will be crucial that the in vitro experiments are performed in a standardized way to meet regulatory needs. In addition, the chemical and regulatory applicability domains of the in vitro test systems and kinetic models need to be defined. Therefore, it is important that existing protocols are formalized in guidance documents to improve harmonization of testing procedures and correct usage of test results.